Question

if 6 tan A -5 = 0 find the value of( 3 Sin A - Cos A) / (5 Cos A + 9 sin A)

Answer 1

$\textbf{Given:}$

$6\;tanA-5=0$

$\implies\,tanA=\frac{5}{6}$

$\implies\frac{sinA}{cosA}=\frac{5}{6}$

$\text{Then, }sinA=5k\;\;\&\;\;cosA=6k$

$\displaystyle\frac{3\,sinA-cosA}{5\,cosA+9\,sinA}$

$=\displaystyle\frac{3(5k)-6k}{5(6k)+9(5k)}$

$=\displaystyle\frac{15k-6k}{30k+45k}$

$=\displaystyle\frac{9k}{75k}$

$=\displaystyle\frac{3}{25}$

$\implies\boxed{\bf\frac{3\,sinA-cosA}{5\,cosA+9\,sinA}=\frac{3}{25}}$

Answer 2

Step-by-step explanation:

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